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We derive formulas for the general four-center integral and its Bloch sum within the basis of optimally localized muffin-tin orbitals in the atomic spheres approximation. As an example of application the Hartree and exchange energies of silicon are calculated and the cohesive energy determined in the local-density and Hartree-Fock approximations.
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Svane et al. (1986) studied this question.
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